As you may have heard, there are a finite number of IP addresses available to Internet Service Providers (ISP). Once they are all used up, the only way to get more is to reassign them. In technical terms, the limited number of IP addresses refers to the IPv4 address space, while there is plenty of room in the IPv6 address space.
Until ISPs begin fully adopting IPv6 technology, however, IP addresses will be sold at a premium. The question is: how many do you really need for your dedicated server? The answer really depends on where and how your server is hosted, the number and type of websites you are running, and how you use your server.
For a server with a single enterprise website and one central focus, a single dedicated IP may be all you need. This, however, assumes you also have nameserver IPs on another machine or from a service. If your server is housed in a remote datacenter, your nameservers may be managed by the provider. If not, you will need at least two IP addresses.
If you have more than one website, you can usually use shared IPs for most of them, unless they require SSL for ecommerce or community logins. For encrypted sites, you will need an IP for each one, if you want authenticated SSL certificates.
If you are using your server for web hosting, you may need to regularly acquire IP addresses for your customers, and you should use a service that will allow you to quickly and easily add more. Often times, you can purchase them in bulk, depending on the number you need.
It is a good idea to know ahead of time how many IP addresses you think you might want, but even if you repurpose your server at a later date, you should still be able to add more IPs without any difficulty.